Ministry spokesman Igor Konashenkov told reporters that the plane wreck was located 70 meters beneath the Black Sea and that rescue squads have so far recovered four bodies.
"Debris from the Tu-154 was found 1.5 kilometers from the coast of Sochi," Russia's official TASS news agency earlier quoted emergency services as saying.
According to Konashenkov, the plane took off from Adler Airport in the coastal resort city of Sochi at 5.25 a.m., (0225GMT), and disappeared from radar two minutes later.
The list of passengers on board the Tu-154 released by the ministry includes 64 musicians from the Red Army Choir or Alexandrov Ensemble, as well as nine journalists, eight soldiers, two ministry officials, and one member of an NGO.
Search efforts are underway with air and naval support from Russian vessels and helicopters.
The cause of the crash is not yet known.
Kremlin spokesman Dmitry Peskov told reporters that President Vladimir Putin was informed about the incident.
The plane was en route to Syria’s Latakia province for a Christmas concert.
The Red Army Choir last performed in Turkey in 2015.